Applied Formal Methods Researcher (Lean 4)
Posted Today by Alignerr
Negotiable
Undetermined
Remote
Manchester, England, United Kingdom
Summary: The role of Applied Formal Methods Researcher focuses on translating mathematical proofs into machine-verifiable formats using Lean 4, contributing to advanced AI reasoning research. This fully remote position is designed for mathematicians passionate about formal verification and involves pushing the limits of proof assistants. Researchers will analyze and construct formalizations, collaborate with peers, and document their findings to enhance formal verification processes. The position offers flexibility in hours and the opportunity to work on cutting-edge AI projects.
Key Responsibilities:
- Translate informal mathematical proofs into clean, structured, machine-verifiable formalizations in Lean 4.
- Analyze proofs across domains, identifying gaps, hidden assumptions, and formalizable sub-structures.
- Construct formalizations that test the boundaries of existing proof assistants.
- Investigate and articulate why automated provers struggle or fail.
- Collaborate with researchers to design and refine strategies that improve formal verification pipelines.
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms.
- Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models.
- Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments.
- Surface deeper patterns and generalizations that become visible only through formalization.
Key Skills:
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
- Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics.
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable proof assistant.
- Able to translate dense, informal mathematical arguments into precise, structured formal proofs.
- Genuinely enthusiastic about formal verification, proof assistants, and mechanized mathematics.
- Mathematically mature and comfortable working at the frontier of automated tools.
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools (nice to have).
- Experience contributing to large-scale formalization projects such as Mathlib (nice to have).
- Strong written communication skills for documenting formalization decisions and reasoning strategies (nice to have).
Salary (Rate): £140.00 hourly
City: Manchester
Country: United Kingdom
Working Arrangements: remote
IR35 Status: undetermined
Seniority Level: undetermined
Industry: IT
About The Role
What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable proofs in Lean 4 — working at the very edge of what automated reasoning can do today. This is a fully remote, flexible contract role built for mathematicians who live and breathe formal verification. You'll work on proofs that push proof assistants to their limits, helping map the frontier of mechanized mathematics and contributing to some of the most technically demanding AI research happening right now.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into clean, structured, machine-verifiable formalizations in Lean 4
- Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the boundaries of existing proof assistants, especially where automation breaks down
- Investigate and articulate why automated provers struggle or fail — complexity, missing lemmas, library gaps, and beyond
- Collaborate with researchers to design and refine strategies that improve formal verification pipelines
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
- Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
- Surface deeper patterns and generalizations that become visible only through formalization
Who You Are
- Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable proof assistant — Lean strongly preferred
- Able to translate dense, informal mathematical arguments into precise, structured formal proofs
- Genuinely enthusiastic about formal verification, proof assistants, and the trajectory of mechanized mathematics
- Mathematically mature and comfortable working at the frontier — where automated tools fall short and human insight is essential
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience contributing to large-scale formalization projects such as Mathlib
- Exposure to theorem provers in settings where manual scaffolding is frequently required
- Prior experience with data annotation, evaluation systems, or data quality workflows
- Strong written communication skills for documenting formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work on cutting-edge AI projects alongside leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, technically demanding work
- Contribute directly to advancing the state of mechanized mathematics and AI reasoning
- Potential for ongoing work and contract extension as new projects launch